How to resolve the algorithm Prime decomposition step by step in the Modula-2 programming language

Published on 12 May 2024 09:40 PM
#Modula-2

How to resolve the algorithm Prime decomposition step by step in the Modula-2 programming language

Table of Contents

Problem Statement

The prime decomposition of a number is defined as a list of prime numbers which when all multiplied together, are equal to that number.

Write a function which returns an array or collection which contains the prime decomposition of a given number

n

{\displaystyle n}

greater than   1. If your language does not have an isPrime-like function available, you may assume that you have a function which determines whether a number is prime (note its name before your code). If you would like to test code from this task, you may use code from trial division or the Sieve of Eratosthenes. Note: The program must not be limited by the word size of your computer or some other artificial limit; it should work for any number regardless of size (ignoring the physical limits of RAM etc).

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Prime decomposition step by step in the Modula-2 programming language

Source code in the modula-2 programming language

MODULE PrimeDecomposition;

FROM STextIO IMPORT
  SkipLine, WriteLn, WriteString;
FROM SWholeIO IMPORT
  ReadCard, WriteInt;

CONST 
  MaxFacIndex = 31;
(*  2^31 has most prime factors (31 twos) than other 32-bit unsigned integer. *)

TYPE
  TFacs = ARRAY [0 .. MaxFacIndex] OF CARDINAL;

VAR
  Facs: TFacs;
  I, N, FacsCnt: CARDINAL;
  
PROCEDURE CalcFacs(N: CARDINAL; VAR Facs: TFacs; VAR FacsCnt: CARDINAL);
VAR
  I: CARDINAL;
BEGIN
  FacsCnt := 0;
  IF N >= 2 THEN    
    I := 2;
    WHILE I * I <= N DO      
      IF N MOD I = 0 THEN         
        N := N DIV I;
        Facs[FacsCnt] := I; 
        FacsCnt := FacsCnt + 1;
        I := 2      
      ELSE
        I := I + 1
      END
    END;
    Facs[FacsCnt] := N;
    FacsCnt := FacsCnt + 1
  END;
END CalcFacs;

BEGIN
  WriteString("Enter a number: "); 
  ReadCard(N);
  SkipLine;
  CalcFacs(N, Facs, FacsCnt);
  (* There is at least one factor *)
  IF FacsCnt > 1 THEN 
    FOR I := 0 TO FacsCnt - 2 DO 
      WriteInt(Facs[I], 1); 
      WriteString(" ")
    END;
  END;
  WriteInt(Facs[FacsCnt - 1], 1);
  WriteLn
END PrimeDecomposition.

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